The present invention relates to power flow transformers that compensate power flow in a transmission line. More particularly, the present invention relates to a power flow transformer that is simple, versatile, and relatively inexpensive.
Electric power flow through an alternating current transmission line is a function of the line impedance, the magnitudes of the sending-end and the receiving-end voltages, and the phase angle between such voltages, as shown in FIG. 1. The impedance of the transmission line is typically inductive; accordingly, power flow can be decreased by inserting an additional inductive reactance in series with the transmission line, thereby increasing the effective reactance of the transmission line between its two ends. The power flow can also be increased by inserting an additional capacitive reactance in series with the transmission line, thereby decreasing the effective reactance of the transmission line between its two ends. The indirect way to emulate an inductive or a capacitive reactance is to inject a voltage in quadrature with the prevailing line current.
The direct method of voltage regulation of a transmission line is to add a compensating voltage vectorially in- or out-of-phase with the voltage of the transmission line at the point of connection. The indirect method to regulate the line voltage is to connect a capacitor or an inductor in shunt with the transmission line. A shunt-connected capacitor raises the line voltage by way of generated reactive power. A shunt-connected inductor absorbs reactive power from the line and thus lowers the voltage. The indirect way to implement a shunt capacitor or inductor is to generate a voltage in phase with the line voltage at the point of connection and connect the voltage source to the line through an inductor. Through control action, the generated voltage can be made higher or lower than the line voltage in order to emulate a capacitor or an inductor. Lastly, inserting a voltage in series with the line and in quadrature with the phase-to-neutral voltage of the transmission line can change the effective phase angle of the line voltage.
In order to regulate the voltage at any point in a transmission line, an in-phase or an out-of-phase voltage in series with the line is injected. FIG. 2 shows the shunt compensating transformer scheme for voltage regulation in a transmission line. The exciter unit consists of a three-phase Y-connected primary winding, which is impressed with the initial line voltage, v1xe2x80x2(i.e., v1Axe2x80x2, v1Bxe2x80x2, and VCxe2x80x2). The shunt-compensating unit consists of a total of six secondary windings (two windings in each phase for a bipolar voltage injection). The line is regulated at a voltage, v1 by adding a compensating voltage, v11xe2x80x2, either in- or out-of-phase with the line voltage. The bipolar compensating voltage in any phase is induced in two windings placed on the same phase of the transformer core. To control the shunt compensating unit, a reference voltage V1* is fed to a gate pattern logic which monitors the magnitude V1xe2x80x2 of the exciter voltage, v1xe2x80x2, and determines the number of turns necessary on the shunt compensating unit. Based on this calculation, an appropriate thyristor valve is switched on in a tap changer (FIG. 3), which puts the required number of turns in series with the line.
FIG. 3 shows the schematic diagram of a thyristor-controlled tap changer. A transformer winding is tapped at various places. Each of the tapped points is connected to one side of a back-to-back thyristor (triac) switch. The other sides of all the thyristor switches are connected together at point A. Depending on which thyristor is on, the voltage between points A and B can be varied between zero and the full winding voltage with desired steps in between. In a mechanical version of this arrangement, a load tap changer connects with one of a number of taps to give a variable number of turns between the connected tap and one end of the winding.
A Static VAR Compensator (SVC) consists of a series of inductors and capacitors as shown in FIG. 4. SVC compensation is achieved by putting either inductance or capacitance in the circuit through a thyristor switch. The level of compensation is determined by adjusting the conduction angle of the thyristor switch.
A static synchronous compensator (STATCOM) is a voltage source converter (VSC) coupled with a transformer as shown in FIG. 5. Such STATCOM injects an almost sinusoidal current of variable magnitude at the point of connection with a transmission line. Such injected current is almost in quadrature with the line voltage, thereby emulating an inductive or a capacitive reactance at the point of connection with the transmission line.
The STATCOM is connected at BUS 1 of the transmission line, which has an inductive reactance, Xs, and a voltage source, Vs, at the sending end and an inductive reactance, Xr, and a voltage source, Vr, at the receiving end, respectively. The STATCOM consists of a harmonic neutralized voltage source converter, VSC1, a magnetic circuit, MC1, a coupling transformer, T1, a mechanical switch, MS1, current and voltage sensors, and a controller. The primary control of VSC1 is such that the reactive current flow through the STATCOM is regulated.
The STATCOM controller operates the VSC such that the phase angle between the VSC voltage and the line voltage is dynamically adjusted so that the STATCOM generates or absorbs desired VAR at the point of connection. FIG. 6 shows a simplified diagram of the STATCOM with a VSC voltage source, E1, and a tie reactance, XTIE, connected to a power system with a voltage source, VTH, and a Thevenin reactance, XTH. When the VSC voltage is higher than the power system voltage, the system xe2x80x9cseesxe2x80x9d the STATCOM as a capacitive reactance and the STATCOM is considered to be operating in a capacitive mode. Similarly, when the power system voltage is higher than the VSC voltage, the system xe2x80x9cseesxe2x80x9d the STATCOM as an inductive reactance and the STATCOM is considered to be operating in an inductive mode.
The effective line reactance is varied directly by using either mechanically switched or thyristor switched inductors and capacitors, such as those found in a Thyristor Controlled Series Compensator (TCSC) as shown in FIG. 7. The basic implementation of a TCSC consists of one or a string of capacitor banks, each of which is shunted by a Thyristor Controlled Reactor (TCR). In this arrangement, the current through a TCR, which also circulates through the associated capacitor bank, is varied in order to control the compensating voltage and thus the variable reactance. A STATCOM and the STATCOM model are disclosed in more detail in Sen, STATCOMxe2x80x94STATic synchronous COMpensator: Theory, Modeling, and Applications, IEEE Pub. No. 99WM706, hereby incorporated by reference.
A Static Synchronous Series Compensator (SSSC) is a Voltage Source Converter coupled with a transformer as shown in FIG. 8. An SSSC injects an almost sinusoidal voltage, of variable magnitude, in series with a transmission line. This injected voltage is almost in quadrature with the line current, thereby emulating indirectly an inductive or a capacitive reactance, Xq, in series with the transmission line as shown in FIG. 9. The compensating reactance, Xq, has a positive value when emulating a capacitor and a negative value when emulating an inductor. The effective line reactance, Xeff, has a positive value when being inductive and a negative value when being capacitive.
The SSSC is connected in series with a simple transmission line, which has an inductive reactance, Xs, and a voltage source, Vs at the sending-end and an inductive reactance, Xr, and a voltage source, Vr, at the receiving-end, respectively. The SSSC consists of a harmonic neutralized Voltage Source Converter, VSC2, a magnetic circuit, MC2, a coupling transformer, T2, a mechanical switch, MS2, one electronic switch, ES, current and voltage sensors, and a controller. The primary function of the SSSC is to inject a voltage in series with the transmission line and in quadrature with the prevailing line current.
FIG. 9 shows a simple power transmission system with an SSSC operated both in inductive and in capacitive modes and the related phasor diagrams. The line current decreases from I0% to Ixe2x88x92100%, when the inductive reactance compensation, xe2x88x92Xq/XL, increases from 0% to 100%. The line current increases from I0% to I33%, when the capacitive reactance compensation, Xq/XL, increases from 0% to 33%. An SSSC and the SSSC model are disclosed in more detail in Sen, SSSCxe2x80x94Static Synchronous Series Compensator: Theory, Modeling, and Applications, IEEE Pub. No. PE-862-PWRD-0-04-1997, hereby incorporated by reference, and in Gyugyi, Schauder, and Sen, SSSCxe2x80x94Static Synchronous Series Compensator: A Solid-State Approach to the Series Compensation of Transmission Lines, IEEE Pub. No. 96WM120-6PWRD, also hereby incorporated by reference.
The effective angle of a transmission line is varied by using a Phase Shifting Transformer, which is also known as a Phase Angle Regulator (PAR). A PAR injects a voltage in series with the transmission line and in quadrature with the phase-to-neutral voltage of the transmission line as shown in FIG. 10A. The series injected voltage introduces a phase shift whose magnitude in radian varies with the magnitude of the series injected voltage input where the phase-to-neutral voltage of the transmission line is the base voltage. In a typical configuration, a PAR consists of two transformers (FIG. 10B). The first transformer in the exciter unit is a regulating transformer that is shunt connected with the line. The first, regulating transformer primary windings are excited from the line voltage and a voltage is induced in the secondary windings. A voltage with variable magnitude and in quadrature with the line voltage is generated from the phase-to-phase voltage of the induced voltage of the first transformer using taps. For series injection of this voltage, an electrical isolation is necessary.
The second transformer in the series unit is a series transformer that is excited from the phase-to-phase voltage of the regulating transformer and its induced voltage is connected in series with the line. Since the series injection voltage is only a few percent of the line voltage, the series transformer can be a step-down transformer. The primary winding of the series transformer as well as the secondary winding of the regulating transformer can be high voltage and low current rated so that the taps can operate normally at low current and can ride through high fault current.
In an alternate arrangement as shown in FIG. 10C, the PAR regulates the angle of the transmission line voltage using two transformers maintaining equal lengths of phasors V1, and V2. In another arrangement as shown in FIG. 10D, there may be two series connected windings, which are dedicated for inducing a compensating voltage for series injection in each phase. In this way, there are three pairs of electrically isolated windings for the series unit (one pair for each phase) and three windings for the exciter unit. This arrangement uses only a single-core three-phase transformer. However, the taps carry high line current as well as even higher fault current. The capability of the PAR shown in FIG. 10D can be achieved in an alternate arrangement shown in FIG. 10E where the exciter unit is delta-connected, which offers fewer windings and no ground connection.
The characteristics of mechanically switched and Thyristor-controlled Power Flow Controllers are such that each controller can control only one of the three transmission parameters (voltage, impedance, and angle). Therefore, changing one parameter affects both the real and the reactive power flow in the transmission line.
The desired operation of an ideal power flow controller is described below. FIG. 11A shows a single line diagram of a simple transmission line with an inductive reactance, XL, and a series insertion voltage, Vdq, connecting a sending-end voltage source, Vs, and a receiving-end voltage source, Vr, respectively. The voltage across the transmission line reactance, XL, is Vx=Vsxe2x88x92Vrxe2x88x92Vdq=IXL where I is the current in the transmission line. Changing the insertion voltage, Vdq, in series with the transmission line can change the voltage, Vx, across the transmission line and, consequently, the line current and the power flow in the line will change.
Consider the case where Vdq=0 (FIG. 11, section (b)). The transmission line sending-end voltage, Vs, leads the receiving-end voltage, Vr, by an angle xcex4. The resulting current in the line is I; the real and the reactive power flow at the receiving end are P and Q, respectively. With an injection of Vdq in series with the transmission line, the transmission line sending-end voltage, Vo still leads the receiving-end voltage, Vr, but by a different angle xcex41 (FIG. 11, section (c)). The resulting line current and power flow change, as shown. With a larger amount of Vdq injected in series with the transmission line, the transmission line sending-end voltage, Vo, now lags the receiving-end voltage, Vr, by an angle xcex42(FIG. 11, section (d)). The resulting line current and the power flow now reverse. Notice that the injected series voltage, Vdq, is at any angle, "PHgr", with respect to the line current, I. This necessitates the series injected voltage to exchange both real and reactive power with the transmission line, which emulates, in series with the line, a capacitor or an inductor and a positive resistor that absorbs real power from the line or a negative resistor that delivers real power to the line. The result is that the real and the reactive power flow in the line can be regulated selectively. Recall an SSSC injects a voltage in quadrature with the line current and, therefore, affects both the real and the reactive power flow in the line simultaneously.
For a desired amount of real and reactive power flow in a line, a single compensating voltage with a variable magnitude and at any angle with respect to the line current should be injected in series with the line. The compensating voltage, being at any angle with the prevailing line current, emulates in series with the transmission line a capacitor, an inductor, a positive resistor that absorbs real power from the line and a negative resistor that delivers real power to the line. Since the line current is at any angle with respect to the line voltage, the compensating voltage is also at any angle with respect to the line voltage. Note that the necessary condition to selectively regulate the real and reactive power flow in the line is that the series injected voltage must be at any angle with respect to the prevailing line current. Also note that the series injected voltage in FIG. 9 is at some arbitrary angle with respect to the line voltage, Vs, but the line current is always in quadrature with the series injected voltage, which affects both the real and the reactive power flow in the line at the same time.
When the STATCOM of FIG. 5 and the SSSC of FIG. 8 operate as stand-alone compensators, they exchange almost exclusively reactive power at their terminals. While operating both the VSCs together as a unified power flow controller (UPFC) with a common DC link capacitor, as shown in FIG. 12, the exchanged power at the terminals of each inverter can be reactive as well as real. The exchanged real power at the terminals of one VSC with the line flows to the terminals of the other VSC through the common DC link capacitor. The DC capacitor voltage is defined by the reactive current flowing through the STATCOM. The variable series injected voltage is derived from the DC capacitor voltage and can be at any angle with respect to the line current.
FIG. 12 shows a UPFC connected in series with a simple transmission line, which has an inductive reactance, Xs, and a voltage source, Vs at the sending-end and an inductive reactance, Xr, and a voltage source, Vr, at the receiving-end, respectively. The UPFC consists of two harmonic neutralized voltage source converters, VSC1 and VSC2, two magnetic circuits, MC1 and MC2, two coupling transformers, T1 and T2, four mechanical switches, MS1, MS2, MS3, and MS4, one electronic switch, ES, current and voltage sensors, and a controller. The VSCs are connected through a common DC link capacitor. The STATCOM is operated by regulating the reactive current flow through it. The SSSC is operated by injecting a voltage in series with the transmission line.
FIG. 13 shows a basic UPFC model, which consists of a STATCOM and an SSSC. The SSSC injects a voltage, Vdq, in series with the transmission line, which, in turn, changes the voltage, Vx, across the transmission line and hence the current and the power flow through the transmission line change. FIG. 13 also shows a phasor diagram of a simple power transmission system, defining the relationship between the sending-end voltage, Vs, the receiving-end voltage, Vr, the voltage across XL, Vx, and the inserted voltage, Vdq, with controllable magnitude (0xe2x89xa6Vdqxe2x89xa6Vdqmax) and angle (0xe2x89xa6xcfx81 xe2x89xa6360xc2x0). The inserted voltage, Vdq, is added to the fixed sending-end voltage, Vs, to produce the effective sending-end voltage, Vo=Vs+Vdq. The difference, Voxe2x88x92Vr, provides the compensated voltage, Vx, across XL. As angle xcfx81 is varied over its full 360xc2x0 range, the end of phasor Vdq moves along a circle with its center located at the end of phasor Vs. The rotation of phasor Vdq with angle xcfx81 modulates both the magnitude and the angle of phasor Vx and, therefore, both the transmitted real power, P, and the reactive power, Q, vary with xcfx81 in a sinusoidal manner. The phase angle, xcfx86, (FIG. 11, sections (c) and (d)) between the injected voltage, Vdq, and the line current, I, can vary between 0 and 2xcfx80. The component of the injected voltage, which is in or out of phase with the line current, emulates a positive or negative resistor in series with the transmission line. The remaining component, which is in quadrature with the line current, emulates an inductor or a capacitor in series with the transmission line. This process, of course, requires the compensating voltage, Vdq, to deliver and absorb both real and reactive power, Pexch and Qexch, which are also sinusoidal functions of angle xcfx81 (Pexch being shown in FIG. 13 since only the real power flows through the DC link capacitor). The exchanged real power, Pexch, and reactive power, Qexch, by the SSSC with the line are
Pexch=Vdqxc2x7I=Vdq/cosxcfx86=Vd/, and
Qexch=Vdqxc3x97I=Vdq/sinxcfx86=Vq/.
Only the exchanged real power, Pexch, with the line flows through the STATCOM. This real power flow through the STATCOM results in a corresponding real current, Id, flow which is either in-phase or out-of-phase with the line voltage. The loading effect of such real current Id on the power system network may be compensated by the independent control of the reactive current flow through the STATCOM. This reactive or quadrature component, Iq, which is in quadrature with the line voltage, emulates an inductive or a capacitive reactance at the point of connection with the transmission line. A UPFC and the UPFC model are disclosed in more detail in Sen and Stacey, UPFCxe2x80x94Unified Power Flow Controller: Theory, Modeling, and Applications, IEEE Pub. No. PE-282-PWRD-0-12-1997, hereby incorporated by reference.
While the PAR of FIGS. 10A-10E and the UPFC of FIG. 12 are useful schemes for power flow control in a transmission line of a power transmission system, it is to be recognized that such schemes are deficient in such areas as versatility, simplicity, and relative cost. Accordingly, a need exists for a power flow control scheme that is in fact more versatile, simpler, and relatively inexpensive.
In the present invention, the aforementioned need is satisfied by a power flow transformer (PFT) based on the traditional technologies of transformers and tap changers. By using a PFT, one can selectively control the real and the reactive power flow in a line and regulate the voltage of the transmission line. Such PFT generates a compensating voltage of line frequency for series injection with a transmission line. Such compensating voltage is extracted from the line voltage and is of variable magnitude and at any angle with respect to the line voltage. The compensating voltage is also at any angle with respect to the prevailing line current, which emulates, in series with the line, a capacitor, an inductor, a positive resistor that absorbs real power from the line, or a negative resistor that delivers real power to the line. Accordingly, the real and the reactive power flow in a transmission line can be regulated selectively.
In one embodiment of the present invention, a limited-angle power flow transformer implements power flow control in a transmission line of an n-phase power transmission system, where each phase of the power transmission system has a transmission voltage. The transformer has n primary windings, where each primary winding is on a core and receives the transmission voltage of a respective one of the phases of the power transmission system. The transformer also has m secondary windings on the core of each primary winding for a total of m*n secondary windings, where m is less than n. Each secondary winding has a voltage induced thereon by the corresponding primary winding.
For each phase, m secondary windings are assigned to the phase. Each assigned secondary winding for the phase is from a different core. For all phases, the secondary windings are assigned from the cores in a balanced manner. For each phase, the secondary windings assigned to the phase are coupled in series for summing the induced voltages formed thereon. The summed voltage is a compensating voltage for the phase, and the compensating voltage is angularly limited with respect to the phase.
Generally, in the PFT, regulation of a transmission line voltage is achieved by adjusting the number of turns in a nine-winding set by way of mechanical or solid-state tap changers. Although mechanical tap changers are quite adequate for most utility applications, dynamic performance can be improved if need be by employing solid-state tap changers such as thyristor-controlled switches.